Holomorphic and Meromorphic Mappings and Curvature. II.
Holomorphic Automorphisms of Compact Kähler Surfaces and Their Induced Actions in Cohomology.
Holomorphic Cartan geometries and rational curves
We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold. This shows that many complex manifolds admit no or few holomorphic Cartan geometries.
Holomorphic equivariant cohomology.
Holomorphic group actions with many compact orbits.
Holomorphically pseudosymmetric Kähler metrics on ℂℙⁿ
The aim of this paper is to present examples of holomorphically pseudosymmetric Kähler metrics on the complex projective spaces ℂℙⁿ, where n ≥ 2.
Homogeneous bundles and the first eigenvalue of symmetric spaces
In this note we prove the stability of the Gieseker point of an irreducible homogeneous bundle over a rational homogeneous space. As an application we get a sharp upper estimate for the first eigenvalue of the Laplacian of an arbitrary Kähler metric on a compact Hermitian symmetric spaces of ABCD–type.
Homogeneous Kähler manifolds admitting a transitive solvable group of automorphisms
Homogeneous totally real submanifolds of complex projective space
Hyper Kähler and quaternionic Kähler geometry.
Hyperbolicity of negatively curved Kähler manifolds.
Hyperholomorphic connections on coherent sheaves and stability
Let M be a hyperkähler manifold, and F a reflexive sheaf on M. Assume that F (away from its singularities) admits a connection ▿ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [21]. Such sheaves are stable and their singular sets are hyperkähler subvarieties in M. In the present paper, we study sheaves admitting a connection with SU(2)-invariant...
Hyperkähler manifolds